David Tall : Life |
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TRAVELLING TO TALK For ten years as an academic (1966-76) I attended only the occasional local and national conferences to listen to others. We were living on only my salary and, frankly, I had no intention spending family money on travelling for my university work. This was a serious business. An international conference might cost £100 and the university would offer a half. Yet my take home salary was only £100 a month at the time and it was all spoken for. I was so engrossed in musical activities in those early years that there was room for little else. Then in 1976 I resigned from the Leamington Spa Opera Group and concentrated on my family and my career. In the same year, for the first time, I was given full financial support to attend my first international meeting, the International Conference in Mathematics Education in Karlsruhe, Germany. Here I had fun. I stayed in a college room to save money and met a student who had his room full of Rheinhessen wine. (He had sold his motorbike to a Winemaker and was paid in kind.) I bought loads at 1 mark 70 for Kabinett and 2 marks 70 for a Spätlese (about half the going rate at the time). It was better quality than the stuff we had at receptions and I freely distributed it amongst other delegates, to widespread approval. At the conference, one of the working groups formed a regular group to meet annually, called the International Group for the Psychology of Mathematics Education (or PME, for short). This has met annually in a different country ever since. In 1977 it was in Utrecht (Holland), then Osnabrück (Germany), then at home at Warwick in 1979. In 1978/9 I had a year's study leave and took the opportunity of visiting contacts in Jerusalem and Montreal. The PME conference in 1980 was in Berkely, California, then Grenoble, France. The following year I worked full-time as a school teacher and was unable to attend, but, by this time, my musical exploits forming the Grainger Society (1978) bore fruit and I was invited in the Summer of 1982 to be a Visiting Fellow in Music at the University of Western Australia, Perth, where I earned my corn by lecturing in music, mathematics, and education. In 1983 PME was in Israel and I was able to visit my uncle's grave in Gaza. Private Denis Tall had been killed by a sniper’s bullet in 1917. His friend standing next to him shot the sniper. Of such futility is war. To travel to Gaza at the time was not considered a sensible act and all my Israeli friends separately begged me not to go. However, I went with three colleagues driving a hire car and we had a wonderful day. The cemetry was spotlessly clean and I was able to bring a small tin of soil back from Denis's grave for my father. It was an uneventful trip. In fact, all the arabs seemed to wave to us as we went past. I reported this to my Israeli friend Dina, who said, “How did they wave?” I hadn‘t noticed. They just waved. ”Was it like this?” asked Dina, waving her hand side to side,“or this?”, waving it forward and backwards. I still didn’t know. She explained further that the first said “Hello,” and the second, “Goodbye.” On reflection, I realised it was the latter. Nevertheless, we drove peacefully through Hebron and had lunch, and then on to the Dead Sea to swim, and on the way back to Jerusalem, we had the radio on listening on the world service to Ian Botham playing a flashy innings for England. In the next couple of years I began to travel around to give seminars in a range of universities in each of Holland, Germany, France, the Netherlands, then back to Israel. Then I had a breakthrough. My earlier work on students conceptualisation of infinite concepts and processes suddenly paid dividends when computer technology arrived. I had bought my own BBC computer in 1982 and, during an enforced ten week rest with back trouble, I began writing software for representing ideas in the calculus. In 1985 I was ahead of the game. Many many others had written calculus sotware, but I had a completely new slant which I called ‘local straightness’. To introduce the idea of the slope of a curved graph, I used the computer to zoom in on it and, as it did so, it got less curved and you could see how steep it was, because it looked like a straight line on the screen. I was invited to a conference in Strassbourg, France, of individuals who had ideas on how to use the computer to teach mathematics. My software was miles and away the best software for drawing graphs, not only technically, but aesthetically, because of the comparative power of the BBC graphics, and also theoretically, because of my knowledge of student thinking processes and my introduction of a new approach. This was the beginning of my reputation for insight into mathematical thinking and the use of the computer and I was invited all over the place. A tour of nine universities in the USA and Canada followed in 1986, including visits to Harvard, Cornell, Montreal, Quebec, Toronto. I got fined for speeding in Quebec. It was rather sad. I was driving back from Quebec to Montreal when I got behind a lorry travelling exactly at the speed limit (100 kph) with no other vehicle in sight. I overtook it and accelerated to draw away and then slow down again. A police car appeared from behind a support on a bridge and stopped me. ”Je vous donnerais un infraction pour la vitesse, m’sieur,” he announced. Then he found I was driving on a British licence not an international one. He then threatened me with driving without a licence. I protested, explaining (en Anglais) that I had a brochure in my car that stated explicitly that a British citizen could drive in Canada for six months on a British Licence. “Mais, ce n’est pas Canada, m’sieur, c’est Québec!”, he asserted triumphantly. However, he found that driving without a license carried a $400 fine and decided that was too steep, settling for a $40 fixed speeding penalty. It is very civilised in Canada. You just go into any bank with the form and hand over $40 plus a $2 handling fee and it is settled. And so it was. Back in Europe my travels grew in intensity — I was invited to be a visiting Professor at Bielefeld University in Germany for two months, including a lecture tour to nearby institutions including several days in Berlin. This was a truly amazing journey. I drove my own car and was warned very seriously about travelling in what was then East Germany. In West Germany the autobahns had no speed limits, so it was quite usual to experience cars shooting past at 200 kph. But then, having crossed into East Germany, the selfsame cares are limited to 100kph. It was amusing to see a sleek black Mercedes drive gingerly past an old smoky Trabant to ease in front without ever going faster than 99kph. We were warned of the ruses of the East German police, desperate for hard western cash, who would fine anyone breaking the law. For instance, there might be a car broken down by the side of the road with a family sitting round looking desperate. However, they were actually part of an elaborate trip to conceal a speed trap. I was told that if I was stopped, for whatever reason, to just pay the fine and go on. In free Berlin, the situation was quite different. There were so many cars that they regularly parked illegally. I found it necessary to do so all the time. On one occasion I was left a fixed 10 mark fine for illegal parking. But my friends told me not to bother as everyone got tickets and no-one paid. On the final day, my host, Roland Stowasser, was in an expansive mood. I wanted to get back to West Germany before dark and was ready to drive away at 9 am but did not manage to take my leave until 3 o’clock in the afternoon! Along the transit road, in the dark, my car engine began to misfire. I had no desire to stop in such an inhospitable place, so I struggled on with my car rolling downhill and spluttering almost to a stop when travelling uphill. Finally I got back to where I was staying and could stop and take a look under the bonnet. The problem was simple. One of the top connectors on a spark plug had come loose and was misfiring. I replaced it and went to bed happy. In the morning I awoke and went to drive into town only to find the battery dead. In my eagerness to look at the problem at night, I had left my sidelights on and this had drained the battery! I took the battery off and walked a couple of kilometres to a garage to struggle with my limited German to ask to get the battery recharged. In the following years, my travels continued. I worked with the Danish Mathematics Association in Copenhagen to introduce a graphic approach to calculus using their own newly developed programs based on my own work. But when they tried to sell versions in Germany, the German academics knew of my software and prevented the publication of materials without my approval. Sofware was also written in Holland for the IBM computer and the programmer, Piet Blokland showed me his own versions at a conference in Sofia Bulgaria. This began a fruitful partnership which included selling the rights in France to the French government for a useful profit. I was continually invited to talk at international venues, including major national and international conferences. In the next years these included the following:
At this point, my illness kept me at home for over a year. But when I was able to get around a little better, the travels began again.
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